As is evident, the photopolymerization reaction in SL resins is very complex. To date, no one has published an analytical photopolymerization model that describes reaction results and reaction rates. However, qualitative understanding of reaction rates is straightforward for simple formulations. Broadly speaking, reaction rates for photopolymers are controlled by concentrations of photoinitiators [I] and monomers [M]. The rate of polymerization is the rate of monomer consumption, which can be shown as [3]:
Rp ¼" d M ½% =dt a M½%k I ½% ðÞ 1=2
where k ¼ constant that is a function of radical generation efficiency, rate of radical initiation, and rate of radical termination. Hence, the polymerization rate is proportional to the concentration of monomer, but is only proportional to the square-root of initiator concentration. Using similar reasoning, it can be shown that the average molecular weight of polymers is the ratio of the rate of propagation and the rate of initiation. This average weight is called the kinetic average chain length, vo, and is given in (4.2):
vo ¼Rp=Ri a M½% = I ½% 1=2